There are fanfics that focus on the physical aspect of their love in a very tasteful way. But more often, the emphasis is on their emotional connection. Some stories show Anakin's love for Padme as his one true anchor in a world that was constantly changing for him. Padme's love for Anakin was also shown as a source of strength for her in the political arena. Different fanfics explore these aspects in various ways, sometimes adding new dimensions to their relationship like how they might have overcome their differences if things had been different in the Star Wars universe.
One portrayal is of a very idealized love. They are shown as the perfect couple, with Anakin always being protective of Padme. Another is a more complex one where their different ideologies, like Anakin's Jedi training conflicting with Padme's political beliefs, add tension to their relationship. And in some fanfics, their love is a doomed love from the start, with the shadow of Anakin's fall to the dark side always looming over them.
In fanfic, their love can be portrayed as a forbidden love that is both exciting and dangerous. Since Jedi are not supposed to have attachments, their relationship is often filled with secrecy. Some fanfics also show how their love was a glimmer of hope in a galaxy filled with war and chaos. It was a love that could have united the Jedi and the political powers, but instead, it was shattered by Anakin's turn to the dark side.